What are the rules of transformation  specifically, of dilation, rotation, reflection and translation?
The rules for translation (shift), rotation, reflection and dilation (scaling) on a twodimensional plane are below.
 Rules of translation (shift)
You need to choose two parameters: (a) center of rotation  a fixed point on a plane and (b) angle of rotation.Once chosen, to construct an image of any point on a plane as a result of this transformation, we have to connect a center of rotation by a vector with our point and then rotate this vector around a center of rotation by an angle congruent to a chosen angle of rotation.
 Rules of reflection
You need to choose two parameters  (a) center of scaling and (b) factor of scaling.Once chosen, to construct an image of any point on a plane as a result of this transformation, we have to connect a center of scaling with our point and stretch or shrink this segment by a scaling factor, leaving the center of scaling in place. Factors greater than 1 will stretch the segment, factors from 0 to 1 are shrinking this segment. Negative factors reverse the direction of a segment to opposite side from the center.
 Rules of reflection
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The rules for transformations are as follows:

Dilation:
 Each point in the original figure is stretched or compressed away from or toward a fixed point called the center of dilation.
 The scale factor determines the amount of stretching or compression.
 If the scale factor is greater than 1, the figure is enlarged.
 If the scale factor is between 0 and 1, the figure is reduced.
 If the scale factor is negative, the figure is reflected across the center of dilation.

Rotation:
 Each point in the original figure is rotated about a fixed point called the center of rotation.
 The angle of rotation determines the amount of rotation.
 Positive angles rotate counterclockwise, while negative angles rotate clockwise.

Reflection:
 Each point in the original figure is reflected across a fixed line called the line of reflection.
 The line of reflection acts as a mirror, with points on one side being reflected onto the other side.

Translation:
 Each point in the original figure is moved a certain distance horizontally and/or vertically.
 The distance and direction of the movement are determined by a vector, which specifies the horizontal and vertical shifts.
These rules are fundamental in understanding how shapes can be transformed in geometry.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 Point A is at #(3 ,2 )# and point B is at #(7 ,3 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
 A line segment goes from #(2 ,6 )# to #(1 ,3 )#. The line segment is dilated about #(2 ,0 )# by a factor of #2#. Then the line segment is reflected across the lines #x = 2# and #y=5#, in that order. How far are the new endpoints from the origin?
 Point A is at #(6 ,1 )# and point B is at #(2 ,8 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
 Points A and B are at #(6 ,2 )# and #(3 ,8 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
 Circle A has a radius of #1 # and a center of #(1 ,2 )#. Circle B has a radius of #2 # and a center of #(5 ,3 )#. If circle B is translated by #<2 ,5 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
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